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3rd order Sallen-Key Low-pass Filter Design Tool
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This page is a web calculator that design a 3rd order Sallen-Key low-pass filter.
Use this utility to simulate the Transfer Function for filters at a given frequency, damping ratio ζ or values of R and C.
The response of the filter is displayed on graphs, showing Bode diagram, Nyquist diagram, Impulse response and Step response.
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<b><font color="#000080">♦</font>Filters</b><br>
<a href="http://sim.okawa-denshi.jp/en/CRlowkeisan.htm">RC LPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/CRhikeisan.htm">RC HPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/LRlowkeisan.htm">LR LPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/LRhikeisan.htm">LR HPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/RLClowkeisan.htm">RLC LPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/RLChikeisan.htm">RLC HPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/RLCbpkeisan.htm">RLC BPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/RLCbekeisan.htm">RLC BEF</a><br>
<a href="http://sim.okawa-denshi.jp/en/OPseikiLowkeisan.htm">Sallen-Key LPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/OPseikiHikeisan.htm">Sallen-Key HPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/Sallenkey3Lowkeisan.htm">3rd order SallenKeyLPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/Sallenkey3Hikeisan.htm">3rd order SallenKeyHPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/OPtazyuLowkeisan.htm">Multiple feedback LPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/OPtazyuHikeisan.htm">Multiple feedback HPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/OPtazyuBakeisan.htm">Multiple feedback BPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/MultipleFB3Lowkeisan.htm">3rd order Multiple feedback LPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/MultipleFB3Hikeisan.htm">3rd order Multiple feedback HPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/TwinTCRkeisan.htm">TwinT notch</a><br>
<a href="http://sim.okawa-denshi.jp/en/CRCRkeisan.htm">CR 2nd order LPF,HPF,BPF</a><br>
<a href="http://sim.okawa-denshi.jp/en/opampkeisan.htm">Active filter</a><br>
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<br>
<font size="-1"><a href="http://sim.okawa-denshi.jp/en/Fkeisan.htm">Filter index</a></font>
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<h5>Calculate the transfer function for 3rd order Sallen-Key low-pass filter with R and C values</h5>
<table class="ss" width="100%">
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<td width="50%">
<table class="ss">
<tbody><tr>
<td>Vi→</td>
<td>
<img src="a500%20%231%20filter%203a_pliki/OPsLow3order.png" border="0">
</td>
<td>→Vo</td>
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Transfer function:<br>
&nbsp;&nbsp;&nbsp;&nbsp;<a href="http://sim.okawa-denshi.jp/images/OPsLowD3.gif">Transfer function of 3rd order Sallen-Key low-pass filter</a><br>
<br>
<br>
<a href="http://sim.okawa-denshi.jp/en/OPseikiLowkeisan.htm">2nd order Sallen-Key low-pass filter tool, use also.</a><br>
</td>
<td width="50%">
<form action="http://sim.okawa-denshi.jp/en/Sallen3tool.php" method="post">
<table class="ss" width="100%"><tbody><tr>
<td width="50%">R1=<input name="p1" maxlength="15" size="9" type="text">Ω</td>
<td width="50%">C1=<input name="p2" maxlength="15" size="9" type="text">F</td>
</tr><tr>
<td width="50%">R2=<input name="p3" maxlength="15" size="9" type="text">Ω</td>
<td width="50%">C2=<input name="p4" maxlength="15" size="9" type="text">F</td>
</tr><tr>
<td width="50%">R3=<input name="R3" maxlength="15" size="9" type="text">Ω</td>
<td width="50%">C3=<input name="C3" maxlength="15" size="9" type="text">F</td>
</tr></tbody></table>
<font size="-1">
p:pico, n:nano, u:micro, k:kilo, M:mega
<br>
<fieldset>
<legend><span>Frequency analysis</span></legend>
<input name="fa1" checked="checked" type="checkbox">Bode diagram<br>
&nbsp;&nbsp;&nbsp;&nbsp;<input name="pgs" value="1" checked="checked" type="radio">Phase&nbsp;&nbsp;<input name="pgs" value="2" type="radio">Group delay<br>
<input name="fa2" checked="checked" type="checkbox">Nyquist diagram<br>
<input name="fa3" checked="checked" type="checkbox">Pole, zero<br>
<input name="fa4" checked="checked" type="checkbox">Phase margin<br>
<input name="fa5" checked="checked" type="checkbox">Oscillation analysis<br>
Analysis on frequency range:<br>
&nbsp;&nbsp;f1=<input name="freqs" maxlength="15" size="10" type="text">∼f2=<input name="freqe" maxlength="15" size="10" type="text">[Hz] (optional)
</fieldset>
<fieldset>
<legend><span>Transient analysis</span></legend>
<input name="ta1" checked="checked" type="checkbox">Step response<input name="ta2" type="checkbox">Impulse response<br>
<input name="ta3" checked="checked" type="checkbox">Overshoot<br>
<input name="ta4" checked="checked" type="checkbox">Final value of the step response<br>
Analysis on time range:<br>
&nbsp;&nbsp;0∼<input name="tim" maxlength="15" size="10" type="text">[sec] (optional)
</fieldset>
<input name="com" value="1" type="hidden">
<p align="right"><input value="Calculate" type="submit"></p>
</font>
</form>
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<hr size="1">
<h5>Calculate the R and C values for the Sallen-Key filter at a given frequency and damping ratio ζ</h5>
<table class="ss" width="100%">
<tbody><tr>
<td width="50%">
<table class="ss">
<tbody><tr>
<td>Vi→</td>
<td>
<img src="a500%20%231%20filter%203a_pliki/OPsLow3order.png" border="0">
</td>
<td>→Vo</td>
</tr>
</tbody></table>
※ 3rd order filters are usually made from combinations of 1st and 2nd order filters following the equivalent block diagram.<br>
<br><br>
Equivalent block diagram:<br>
<br>
<table style="font-size: 12px;"><tbody><tr><td>Vi→</td><td class="waku">2πfc1<br><hr color="#000000" size="1">&nbsp;s+2πfc1&nbsp;</td><td>→</td><td class="waku">(2πfc2)<sup>2</sup><br><hr color="#000000" size="1">&nbsp;s<sup>2</sup>+2ζ(2πfc2)s+(2πfc2)<sup>2</sup>&nbsp;</td><td>→Vo</td></tr></tbody></table>
<br><br>
Transfer function block diagram: <br>
<br>
<img src="a500%20%231%20filter%203a_pliki/OPsLowD3fczeta.gif"><br>
<br>
</td>
<td width="50%">
<form action="http://sim.okawa-denshi.jp/en/Sallen3tool.php" method="post">
<table class="ss" width="100%">
<tbody><tr><td width="100%">
<fieldset>
<legend><span>Select filter type</span></legend>
<input name="settype" value="1" checked="checked" type="radio">Set parameters of the equivalent block diagram
<div class="waku2">
<table class="ss" width="100%">
<tbody><tr><td width="50%">1st order filter:</td><td width="50%"></td></tr>
<tr><td width="50%">&nbsp;&nbsp;f<sub>c</sub>1=<input name="p1" maxlength="15" size="9" type="text">Hz</td><td width="50%"></td></tr>
<tr><td width="50%">2nd order filter:</td><td width="50%"></td></tr>
<tr>
<td width="50%">&nbsp;&nbsp;f<sub>c</sub>2=<input name="p2" maxlength="15" size="9" type="text">Hz</td>
<td width="50%">Damping ratio<br>ζ = <input name="p3" maxlength="15" size="9" value="0.5" type="text"></td>
</tr>
</tbody></table>
<br>
</div>
<input name="settype" value="2" type="radio">Butterworth filter
<div class="waku2">
&nbsp;&nbsp;Cut-off frequency<br>&nbsp;&nbsp;fc=<input name="p4" maxlength="15" size="9" type="text">Hz<br>
</div>
<input name="settype" value="3" type="radio">Chebyshev filter
<div class="waku2">
&nbsp;&nbsp;Characteristic frequency<br>&nbsp;&nbsp;fc=<input name="p5" maxlength="15" size="9" type="text">Hz<br>
&nbsp;&nbsp;Gain ripple gr=<input name="p6" maxlength="15" size="9" type="text">dB<br>
</div>
<input name="settype" value="4" type="radio">Bessel filter
<div class="waku2">
&nbsp;&nbsp;Characteristic frequency<br>&nbsp;&nbsp;fc=<input name="p7" maxlength="15" size="9" type="text">Hz<br>
</div>
<br>
</fieldset>
</td></tr>
<tr><td width="100%">
<table class="ss" width="100%"><tbody><tr>
<td width="50%">C1 = <input name="C1" maxlength="15" size="9" type="text">F</td>
<td width="50%">C2 = <input name="C2" maxlength="15" size="9" type="text">F</td>
</tr></tbody></table>
C1, C2 is optional. But when setting these capacitances, C1 and C2 of both are needed.<br>
<br>
</td></tr>
<tr><td width="100%">
Select Capacitor Sequence:
<select name="keiretu2">
<option value="6" selected="selected">E6</option>
<option value="12">E12</option>
<option value="24">E24</option>
</select><br>
Select Resistor Sequence:
<select name="keiretu">
<option value="24" selected="selected">E24</option>
<option value="12">E12</option>
<option value="6">E6</option>
<option value="96">E96</option>
</select>
</td></tr>
</tbody></table>
<font size="-1">
<br>
<fieldset>
<legend><span>Frequency analysis</span></legend>
<input name="fa1" checked="checked" type="checkbox">Bode diagram<br>
&nbsp;&nbsp;&nbsp;&nbsp;<input name="pgs" value="1" checked="checked" type="radio">Phase&nbsp;&nbsp;<input name="pgs" value="2" type="radio">Group delay<br>
<input name="fa2" checked="checked" type="checkbox">Nyquist diagram<br>
<input name="fa3" checked="checked" type="checkbox">Pole, zero<br>
<input name="fa4" checked="checked" type="checkbox">Phase margin<br>
<input name="fa5" checked="checked" type="checkbox">Oscillation analysis<br>
Analysis on frequency range:<br>
&nbsp;&nbsp;f1=<input name="freqs" maxlength="15" size="10" type="text">∼f2=<input name="freqe" maxlength="15" size="10" type="text">[Hz] (optional)
</fieldset>
<fieldset>
<legend><span>Transient analysis</span></legend>
<input name="ta1" checked="checked" type="checkbox">Step response<input name="ta2" type="checkbox">Impulse response<br>
<input name="ta3" checked="checked" type="checkbox">Overshoot<br>
<input name="ta4" checked="checked" type="checkbox">Final value of the step response<br>
Analysis on time range:<br>
&nbsp;&nbsp;0∼<input name="tim" maxlength="15" size="10" type="text">[sec] (optional)
</fieldset>
<input name="com" value="2" type="hidden">
<p align="right"><input value="Calculate" type="submit"></p>
</font>
</form>
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